English

Ideal approximation in $n$-exangulated categories

Category Theory 2022-07-28 v1

Abstract

In this paper, we study the ideal approximation theory associated to almost nn-exact structures in the nn-exangulated category. The notions of nn-ideal cotorsion pairs and nn-F\mathbb{F}-phantom morphisms are introduced and studied. In particular, let C\mathscr{C} be an extriangulated category which satisfies the condition (WIC) and T\mathcal{T} be a nicely embedded nn-cluster tilting subcategory of C\mathscr{C}, we prove Salce's Lemma in T\mathcal{T}.

Keywords

Cite

@article{arxiv.2207.13465,
  title  = {Ideal approximation in $n$-exangulated categories},
  author = {Yucheng Wang and Jiaqun Wei},
  journal= {arXiv preprint arXiv:2207.13465},
  year   = {2022}
}

Comments

29 pages. arXiv admin note: text overlap with arXiv:1709.06689 by other authors

R2 v1 2026-06-25T01:16:20.203Z